Param Bonuses

the better the bonus the better the damage if you have that stat leveled.and yes they stack and yes that magic stat ads magic damage to the weapons

Stat bonuses add damage rating to your weapons. The better the letter, the more added damage you get, from nothing to E to S. Some weapons have more than one parametre bonus, and some even have 3 or 4. Usually the bonus isn't really that much of a deal unless its a B, A, or S, or 2 Cs or above.

Str and dex bonus adds to the physical damage, and faith and int to magic. Exceptions of chaos weapons scaling with your humanity, adding to the fire damage. The Dragonslayer Spear scales with str and dex for physical, and faith for lightning damage. One very special weapon, the Chaos Blade, made with Quelaag's soul, scales with dex and humanity, but both add to physical damage. One other rare case is Demon's spear, where it scales only with dex but adds to both physical and lightning damage.

Note that the same letter (B or C) is just a range, so the C bonus from a straight sword may not be the same C bonus for a claymore. This should explain your gargoyle axe and morning star situation.

Magic stat on weapons deal magic damage with normal attacks. That can be the r2 for some catalysts.